Large-Eddy Simulation for Flow andDispersion in Urban Streets

Zheng-Tong Xie 1 & Ian P Castro

School of Engineering Sciences, University of Southampton, SO17 1BJ, UK

Abstract

Large-eddy simulations (LES) with our recently developed inflow approach (Xie &Castro, 2008a) have been used for flow and dispersion within a genuine city area -the DAPPLE site, located at the intersection of Marylebone Rd and Gloucester Plin Central London. Numerical results up to second-order statistics are reported fora computational domain of 1.2km (streamwise) x 0.8km (lateral) x 0.2km (in fullscale), with a resolution down to approximately one meter in space and one secondin time. They are in reasonable agreement with the experimental data. Such a com-prehensive urban geometry is often, as here, composed of staggered, aligned, squarearrays of blocks with non-uniform height and non-uniform base, street canyons andintersections. Both the integrative and local effect of flow and dispersion to thesegeometrical patterns were investigated. For example, it was found that the peaksof spatially averaged urms, vrms, wrms and < u′w′ > occurred neither at the meanheight nor at the maximum height, but at the height of large and tall buildings. Itwas also found that the mean and fluctuating concentrations in the near-source fieldis highly dependent on the source location and the local geometry pattern, whereasin the far field (e.g. >0.1km) they are not. In summary, it is demonstrated thatfull-scale resolution of around one meter is sufficient to yield accurate prediction ofthe flow and mean dispersion characteristics and to provide reasonable estimationof concentration fluctuations.

Key words: street scale flow, street scale dispersion, DAPPLE, wind direction,multiple-tracers

1 INTRODUCTION

Understanding the mechanisms of turbulence, dispersion and heat transfer inurban streets is becoming increasedly important (Arnold et al., 2004; Brit-ter & Hanna, 2003). A number of relevant wind tunnel and field experimentshave been reported in the literature, e.g. Arnold et al. (2004); Cheng & Robins

1 Corresponding author. Email: z.xie@soton.ac.uk; tel: +44(0)23 8059 4493

Preprint submitted to Elsevier Science 28 December 2008

(2004); Rotach et al. (2004); Yee & Biltoft (2004); Carpentieri et al. (2008).Despite their disadvantages compared with experiments, numerical approacheshave numerous advantages, e.g. high controllability, lower cost (sometimes!),three-dimensional/four-dimensional data output. However, Britter & Hanna(2003) point out that computational fluid mechanics studies (i.e. ReynoldsAveraged Navier-Stokes methods-RANS) can sometimes produce reasonablequalitative results for mean flows but the performance, when compared withlaboratory or field experiments, is little better than that of simple operationalmodels. Quite a few researchers in this area have turned to large-eddy simu-lation (LES).

Indeed, LES has demonstrated its capability and potential for such applica-tions, e.g. Baik et al. (2007); Baker et al. (2004); Coceal et al. (2006); Hannaet al. (2002); Kanda et al. (2004); Meinders & Hanjalic (1999); Stoesser et al.(2003); Xie & Castro (2006); Xie et al. (2008c). All of these LES (and directnumerical simulation - DNS) studies focused on flow over simple geometries,e.g. a group of cubes or different height cuboids with the same square base,or a two-dimensional street canyon. These works use simple periodic in-outletboundary conditions for which it is assumed that the computational domainis one repeated unit of the whole urban geometry, or a very simple inflowboundary condition without proper correlation in time and in space. Periodicboundary conditions may generate severely biased results for a genuine urbandomain with a limited size, e.g. for DAPPLE site (not reported in this paper).Inflow specified at the inlet without proper correlations in time or in spacehave been shown in the literature to be inadequate, as we confirmed in Xie &Castro (2008a).

As a reasonable start to gain a deeper insight to the dispersion mechanismsin urban environments, it is useful to investigate the flow over typical pat-terns of urban geometry, e.g. street canyons (Baik et al., 2007; Baker et al.,2004), staggered, aligned or square arrays of blocks with uniform height (Co-ceal et al., 2006; Hanna et al., 2002; Kanda et al., 2004; Meinders & Hanjalic,1999; Stoesser et al., 2003) or non-uniform height (Xie et al., 2008c). However,there is a scarcity of reliable numerical models for flow and dispersion overa genuine urban geometry for understanding the integrative effect of combi-nations of these morphological patterns or for practical purposes. There aresome reports available in the literature on building-resolving LES for genuineurban geometry. Tseng et al. (2006) used LES to predict flow and dispersionin downtown Baltimore, MD with a domain containing about 30 buildings.The inflow velocity field on the inlet plane was obtained from a separate flowsimulation without buildings that uses periodic boundary conditions in thestreamwise direction. The buildings were resolved using 6-8 grid points. Sucha low resolution may not predict the second-order moment statistics accu-rately. And there were no experimental data reported for the validation ofLES in their paper. More recently, Smolarkiewicz et al. (2007) used LES tosimulate dispersion over a 1:200 scale model of the Pentagon building, andcompared LES data with their wind tunnel data. A laminar flow was used for

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the inflow boundary condition of the LES computations. It is not clear howserious are the errors such a simple inflow boundary condition generates whenthe LES data is used for modelling the full scale case. As far as we are aware,no comprehensive LES work for flow and dispersion over a genuine urban sitehas been performed and validated quantitatively against experiments.

In order to establish the credibility of LES as a tool for operational/practicalforecast applications, there are many issues which must be addressed, suchas: 1. Is there a general minimum resolution to produce reasonable turbulencestatistics? If the answer is ‘YES’ for the flow, is it also applicable for scalardispersion? 2. Is LES reliable for high Reynolds number? 3. How much doesLES accuracy depend on the mesh resolution and quality? 4. What is themost appropriate inflow boundary condition? 5. Should coupling between theweather scale flow and the urban boundary layer be achieved?

Recently an LES model implemented in major commercial codes was used tocalculate the turbulent flow over staggered wall-mounted cubes and a stag-gered array of random height obstacles with an area density 25% (Xie & Cas-tro (2006), hereafter denoted XC). It was found that a significantly coarsermesh (e.g. approximately 20 × 20 × 20 grid points per building block) thanrequired for a full DNS produced sufficiently accurate results. Turbulence gen-erated by urban-like obstacles, e.g. cuboid-shape bodies with sharp edges,is building-block-scale dominated and viscous effects (on the building sur-faces, for example) are insignificant, so that for this type of flow the precisewall condition/subgrid-scale model is unimportant for capturing the building-block-scale flows and surface drag. The results also confirm that Reynoldsnumber dependency of such flows (if it does exist) is very weak, as suggestedalso by wind tunnel experiments. Such complex wall flows are thus, paradox-ically, significantly easier to compute with LES than are smooth-wall flows,where viscous effects dominate near the wall. These issues are fully discussedin XC.

In the present paper, flow and point source dispersion over a genuine urbangeometry – the DAPPLE site (http://www.DAPPLE.org.uk) – were simu-lated numerically using LES. There were more than fifty building obstacles(including a dome and a tower) in the DAPPLE site. The first issue was howto fulfil the resolution requirement without exceeding the available computer’scapability. The mean building height of DAPPLE was 22 meter. As we hadpreviously concluded that roughly 20×20×20 grids points per building blockproduces sufficiently accurate results for such flows (see XC), a resolution downto one meter was chosen for the LES. Our objective is to simulate flow andpollutant dispersion within genuine urban canopy regions. Such a localisedcomputational domain may in fact be smaller than the typical city size. Thisexacerbates the difficulties posed by having to supply appropriate boundaryconditions. One requires an efficient method to insert appropriate small-scaleturbulence at the upstream boundary at each time step, recognising that theflow is almost never close to being spatially periodic. Our final objective is

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coupling weather-scale computations (for example from the UK Met Office’sweather code, the Unified Model – UM) to smaller-scale computations of flowand dispersion within urban environments. This also requires a particularlyefficient means of providing dynamically changing turbulence data at the inletof the computational domain. A new inflow technique (Xie & Castro, 2008a)has been used for all the LES computations reported here.

In the following sections, firstly a very brief description of the governing equa-tions is given in §2; secondly, numerical settings including geometry and meshare given in §3; thirdly, inflow conditions are given in §4; fourthly, LES forDAPPLE is validated in §5; fifthly, §6 describes numerical experiments per-formed to investigate the sensitivity to wind direction, inflow condition, sourcelocation, etc; finally in §7 concluding remarks are given.

2 Governing equations

To ensure a largely self-contained paper, a brief description of the governingequations of LES is given here. More details can be found in XC. The filteredcontinuity and Navier-Stokes equations are written as follows,

∂ui

∂xi

= 0

∂ui

∂t+

∂uiuj

∂xj

= −1

ρ

(∂p

∂xi

)+

∂

∂xj

(τij + ν

∂ui

∂xj

).

(1)

The dynamical quantities, ui, p are resolved-scale (filtered) velocity and pres-sure respectively. ν is the kinematic viscosity. In the near-wall region, the Lillydamping function was also applied. τij is the subgrid-scale (SGS) Reynoldsstress. The Smagorinsky SGS model was used, τij − δijτkk/3 = 2ρ(Cs∆)2

(2smn smn)1/2sij, where sij = 12(∂ui

∂xj

+∂uj

∂xi

); ∆ is taken as the cubic root of

the cell volume; Cs = 0.1, which is recommended by Shah (1998) for flowpast a blunt obstacle. τkk is modelled according to a closure similar to theone devised by Yoshizawa (1986). δij is the Kronecker-delta. In our previouspaper - XC, we argue because such flows are block-scale dominant so that,provided the grid is sufficiently resolved to capture much of the inertial rangein the spectrum, the LES results are insensitive to the precise form of the SGSmodel.

For cases where the fine eddies in the vicinity of the wall are important, it isrecommended that N +

1 is of order of unity (N +1 is the distance in wall units

between the centroid of the first cell and the wall assuming the N coordinateis normal to the wall). Note, however, that for a complex geometry, whereseparation and attachment processes occur, it is impossible to satisfy this

4

criteria everywhere. We argue that, unlike the situation for smooth-wall flows,it is in fact not necessary, at least for obtaining overall surface drag and theturbulent motions at the scale of the roughness elements (buildings), whichturn out to be dominant (see XC).

The filtered governing equation for the scalar is written as follows,

∂c

∂t+

∂uj c

∂xj

=∂

∂xj

[(Ks + Km)

∂c

∂xj

]+ S (2)

where Ks and Km are the subgrid turbulent diffusivity and molecular diffusiv-ity respectively and S is the source term. Up to now most studies for concen-tration dispersion problems have applied a subgrid eddy viscosity combinedwith a subgrid scale Schmidt number, which are set as constant or calculateddynamically. In the present study, we adopt this approach using a constantsubgrid scale Schmidt number of unity. Km is small in our simulation, sincethe Reynolds number is large, but that term is nevertheless included.

3 Numerical settings

The entire LES model was implemented in the code described in XC. Crucially,the discretisation for all terms in Eq. (1, 2) was second order accurate in bothspace and time. The convective terms in Eq. (1, 2) were discretized in spaceusing the 2nd order monotone advection and reconstruction scheme (MARS).An efficient inlet turbulence generation scheme (Xie & Castro, 2008a) wasused, with symmetric conditions at the lateral boundaries and a stress-freeboundary at the top (z = 10hm, where hm is the mean height of the buildingsin the domain - 110mm in the 1:200 scale model used, see below). The topboundary condition here is simple but widely used in literature, e.g. Moeng(1984). The artificial boundary condition may be interpreted as a strong in-version. A detailed setting of the inflow approach can be found in §4. TheReynolds number based on hm and the free stream velocity Uref was approxi-mately 18,000. The time step was 0.003125s, giving an averaged CFL numberof 0.48, and the initial duration of most of the runs was 62.5s with subsequentaveraging over at least 125s for all the statistics.

3.1 Geometry, mesh and resolution.

A description of the DAPPLE field experiment can be found in Arnold et al.(2004). Fig. 1 shows the schematic plan view of the 1:200 scale wind tunnelmodel of the site. Block heights are shown on each. Note the two coordinatesystems used – xt, yt, z is the model system with the xt axis from west to

5

Low resolution model (1:200)

-1500

-1000

-500

0

500

1000

1500

2000

-1500 -1000 -500 0 500 1000 1500 2000 2500

Wes

t (m

m)

Marylebone RdMarylebone Rd

York St

Crawford St

Gloucester P

lG

loucester Pl

x

y

04.51−

88

150

84

150155

55

9068

75

159

100115

120

105

100 75

120

95

320

320

72 70 88 10470

75

108 137

50

8078

83 102

85

125

120

73

93

168128

70

100 87.5 90 10082.58577.5 70

265 110

67.5

90

70

245

Thornton P

l

Regent's Park

Fig. 1. Plan view of the wind tunnel model. Numbers in italics on each buildingblock indicate its height in mm. The model coordinates are marked in mm, with xt

from west to east, yt from south to north and z from ground to top respectively.x, y, z are the computational coordinates (Fig.2).

Fig. 2. Computational domain, with the coordinate origin at the ground at themajor intersection; its size is Lx =6000mm, Ly =4000mm, Lz =1000mm.

east, yt axis from south to north and z axis from ground to top respectively,whereas x, y, z is the computational one, with the x axis from the inlet to theoutlet corresponding to the wind tunnel axis(the wind direction), and the yaxis following the right-hand rule respectively (with z vertical).

Fig. 2 shows the computational domain, which is equivalent to 1200m (stream-wise) x 800m (lateral) x 200m in full scale. Note the computations were con-ducted at wind tunnel size and all the sizes are given in mm if not explicitlydenoted. The mean height of the model buildings (hm) is 110mm and their

6

Fig. 3. Polyhedral mesh. (a) a horizontal plane at z=0; (b) a vertical plane at y=-2m.

packing density is 0.5± 0.001 (Padhra et al., 2008). Because of the lack of ge-ometrical information upstream of the DAPPLE site, three rows of staggered‘artificial’ blocks with height 110mm were installed in the near inlet region.Correspondingly, in the EnFlo wind tunnel a large number of two-dimensionalroughness elements were installed upstream of the DAPPLE site. The artificialblocks were useful to retain a laterally averaged mean velocity profile not toodissimilar in shape to the one imposed at the inlet, which was obtained overthe two-dimensional roughness elements in the wind tunnel. Numerical exper-iments on the sensitivity of the arrangement of the artificial blocks to flowsand scalar dispersion at the intersection of Marylebone Rd and Gloucester Pl,hereafter denoted the major intersection, were performed. The gaps betweenblocks one and two, two and three, and four and five (counting from right toleft looking downstream, see Fig.2) in the second row were entirely blockedby inserting thin solid walls with height hm in the gaps. The other settingswere kept unchanged. The turbulence data and the scalar data were comparedwith those in §5 and it was found that the differences were negligible. Thissuggests that the flow and the scalar dispersion within the DAPPLE site werenot too sensitive to the arrangement of the appropriate artificial blocks whena proper inflow condition with correlations in space and in time is imposed.No artificial building blocks were installed in the near outlet region where,downstream of the DAPPLE site, London’s Regent’s Park was situated.

In order to simulate the flows over a genuine urban canopy with a very complexgeometry, unstructured non-hexahedral meshes inevitably have to be used.Tetrahedral meshes are widely used in CFD because methods which do thisare mature, efficient and highly automated (Peric, 2004). Perhaps not surpris-ingly, it was found that the accuracy of tetrahedral meshes for LES of theseurban-type flows, even at a higher resolution, is not so high as that of uniform

7

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6

(Lx, Ly, Lz)/hm

z/h m

LxLyLz

Fig. 4. Vertical profiles of prescribed integral length scales for LES at inlet.

hexahedra meshes (for equal computational effort) (Xie & Castro, 2008b).Furthermore, unstructured polyhedral meshes offer substantially better prop-erties than tetrahedral meshes (Peric, 2004). A major feature of polyhedralmeshes is that the simplest (and most efficient) approximations that are usedon Cartesian meshes (e.g. linear interpolation, midpoint rule) are applicableand provide nearly the same accuracy as on Cartesian meshes. The flexibilityof polyhedral approach is that the mesh can be optimized in many ways tosatisfy the critical requirements of achieving second order accuracy (e.g. theline connecting two neighbour cell centroids should pass through the centroidof the joint face). Polyhedral meshes in the present case were validated for flowover uniform cubes and then a more random geometry (Xie et al., 2008c).

Fig.3 illustrates how the DAPPLE domain (as shown in Fig.2) was discretizedinto polyhedral cells with three level resolution in the vertical direction andfour level resolution in the streamwise direction. In Fig.3b, the ratios of thegrid size at the first, second and third vertical interfaces (from the inlet to theoutlet) for z < 3hm were approximately 2, 1.4 and 0.5 respectively. The firstand the second interfaces were both upstream of the DAPPLE site, whereasthe third one was downstream. The ratios at the first (i.e. at z = 3hm) and thesecond (i.e. at z = 6hm) horizontal interfaces, which are all above the DAP-PLE site, were approximately 2.5 and 2 respectively. The size of the smallestcells, which were those cells nearest the walls, was approximately hm/15. The2nd order monotone advection and reconstruction scheme (MARS) was usedto eliminate any possible numerical instabilities. We emphasize that the DAP-PLE region itself was meshed essentially uniformly up to a height of 3hm andthe modest discontinuity in mesh sizes elsewhere do not have a significanteffect on the solution accuracy.

4 Inflow conditions

Simulating the flows over a genuine urban region, in particular using a nu-merical weather forecasting code (e.g. the UK Met Office’s Unified Model) to

8

0

1

2

3

4

5

6

7

8

9

10

-0.005 0 0.005 0.01 0.015 0.02

(Reynolds stresses) /Uref2

z/h m

u'u' Expt

w'w' Expt

u'w' Expt

u'u' LES

v'v' LES

w'w' LES

u'w' LES

0

2

4

6

8

10

0 0.5 1 1.5Um/Uref

z/h m

Expt

LES

Fig. 5. Vertical profiles of measured (symbols) and prescribed (lines, for LES atinlet) mean velocity and Reynolds stresses.

provide the dynamic large scale inlet boundary conditions, requires a contin-uous specification of appropriate inlet turbulence. For such computations tobe practical, a very efficient method of generating such turbulence is needed.A digital-filter-based generation of turbulent inflow conditions has been de-veloped and is reported in Xie & Castro (2008a). The artificially generatedturbulent inflows satisfied prescribed integral length scales and a prescribedReynolds stress-tensor.

The inlet integral length scales, which were estimated from Cheng & Castro’scube cases (Castro et al., 2006), are shown in Fig.4. Lx, Ly and Lz are the inte-gral length scales of the axial velocity component in the streamwise, lateral andvertical directions respectively. The mean velocity and the Reynolds stressesat the inlet were obtained by fitting the measured data from the DAPPLEwind tunnel experiments (Cheng & Robins, 2004) and are shown in Fig. 5,where Uref is the free stream velocity. Note that Xie & Castro (2008a) showedthat the computational results are not too dependent on the precise natureof the prescribed length scale profiles, although it is very important that theybe non-zero so that the inlet turbulence has genuine spatial structure.

5 Numerical results and data analysis

5.1 Turbulent flow over the DAPPLE site

From henceforth, all numerical values for specific locations are given in mm,unless otherwise stated. Attention is focused on one wind direction (i.e. -51.4◦

bearing clockwise to the Marylebone Rd direction - approximately southwestwind). The numerically simulated mean velocity and Reynolds stress profilesat fourteen typical stations in the near region of the major intersection (i.e.within ≤ 40m in full scale) were found to be in good agreement with thosefrom the wind tunnel experiments. Fig. 6 shows typical examples of vertical

9

0

1

2

3

4

5

6

-0.5 0 0.5 1Velocity/Uref

Z/h m

Um ExptUm LESVm ExptVm LESWm ExptWm LES

(0,0)

0

1

2

3

4

5

6

-0.01 0 0.01Re stresses/Uref2

u'v' Exptu'v' LESu'w' Exptu'w' LESv'w' Exptv'w' LES

0

1

2

3

4

5

6

0 0.1 0.2r.m.s velocity/Uref

urms Expurms LESvrms Exptvrms LESwrms Expwrms LES

Fig. 6. Vertical profiles of time-mean velocities, velocity fluctuation r.m.s, Reynoldsshear stresses in the model coordinate (xt, yt, z) at the major intersection.

LESExpt.

Fig. 7. Time-mean velocity vectors at z=0.23hm on the major intersection.

profiles of time-mean velocities, velocity fluctuation r.m.s, and Reynolds shearstresses in the model coordinates (xt, yt, z) at the major intersection.

Figure 7 shows a comparison between the LES and the wind tunnel experimentof the time-mean velocity vectors (Um,Vm) on a horizontal plane z = 0.235hm

at the major intersection. The separation bubble on the corner of the southeastbuilding was successfully predicted using LES. However, it was found thatsteady Reynolds Averaged Navier-Stokes equations (RANS) models using thesame mesh as that for LES failed to predict this separation bubble, whichconfirms previous remarks on steady RANS models for such flows, e.g. in XC.

Six 3-D mean streamlines starting at xst = -356, ys

t = -702 and zs = 0, 10, 20,30, 40 and 50 are shown in Fig.8. Here, a streamline is the path that a particleof zero mass would take through the fluid domain driven by the mean velocityvector field. The path was calculated using a Runge-Kutta method. Helical-type streamlines are quite evident. The six pathlines separate significantlyafter a short distance, e.g. 100 mm, which might suggest that the transportof the scalar is sensitive to the source height. However, glancing ahead toFig.14 shows that a large portion of the mean concentration cloud releasedfrom the lowest point source (zs = 10) turns left (looking downstream) atthe first downstream intersection (i.e. York St–Thornton Pl) into the narrowstreet – Thornton Pl. This suggests that we cannot expect to interpret too

10

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

Fig. 8. Time averaged pathlines released at xst = -356, ys

t = 701.9, zs = 0, 10, 20,30, 40 and 50.

much from the ’mean’ pathlines, which don’t of course include any influenceof the turbulent diffusion processes.

Spatially averaged mean velocity and Reynolds stress profiles were obtainedover the region −1000 < xt ≤ 1000,−1000 < yt ≤ 1000 (in which the packingdensity is about 0.53 – slightly greater than that of the whole DAPPLE site)and are shown in Fig. 9. The peaks of urms, vrms, wrms and < u′w′ > occuredat the height 1.5hm, not at the mean building height hm. Note that in thisregion (see Fig.1), there were five large and tall buildings with heights around1.5hm. This confirms the previous finding, e.g. in Xie et al. (2008c), that peaksoccur at the height of the tallest building. Note that it has also been foundthat the tallest buildings provide the dominant contributions to the total dragforce. In the canopy region the temporal r.m.s. velocities are of the sameorder as the mean velocity, which is again consistent with the results in Xieet al. (2008c), where flows over a group of staggered cubes or random heightblocks were investigated. The spatially averaged cross-wind velocity withinand immediately above the canopy is small here, which might be because ofthe random nature of the arrangement of the building blocks.

5.2 Point source dispersion

Five different non-reactive tracers were released at five typical stations – S1(-391, -725, 10), S2 (-356, -702, 10), S3 (0, -600, 10), S4 (0, -500, 10) and S5(-356, -1060, 10), which were all upstream of the major intersection shown inFig.10; numbers in brackets (xt, yt, z) refer to the model coordinates of eachsource. Fig.10 shows a comparison between LES and wind tunnel data forthe mean, normalised concentration at the ten R-locations indicated, for thesource at S2. The coordinates of the R-locations are shown in Table 1. Here themedium mesh is the mesh shown in §3.1. For the fine mesh, in a rectangular

11

0

1

2

3

4

-0.5 0 0.5 1

<Um>/Uref

z/h m

<Um>

<Wm>

<Vm>

0

1

2

3

4

0 0.1 0.2

<urms>, <vrms>, <wrms>/Uref

<urms><vrms><wrms>

0

1

2

3

4

-0.006 -0.004 -0.002 0

<u'w'>/Uref2

<u'w'>

Fig. 9. Vertical profiles of spatially averaged mean velocity, velocity r.m.s. andReynolds shear stress profiles in the computational coordinates x, y, z.

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0 5 10 15 20 25 30

Cm

Ure

fhm

2 /Qs

Wind tunnel data

LES fine mesh

RANS medium mesh

LES medium mesh

R10

R8

R7

R9

R6R2

R1

R3R4

R5

S

S/hm

S=|XR-XS|+|YR-YS|street distance to source;hm mean height;Uref free stream velocity;Qs source flux rate.

S5

Fig. 10. Mean concentration for LES and concentration for RANS at ten DAPPLEstations R1-R10, for which the coordinates are given in Table 1, from source at S2.

Table 1Coordinates in mm of the ten DAPPLE stations R1-R10.

station R1 R2 R3 R4 R5 R6 R7 R8 R9 R10

xt 654 587 130 -43 -72 385 832 1793 43 -288

yt -740 -389 -399 -269 -240 -111 -72 -82 279 -365

zt 7.5 7.5 7.5 7.5 82.5 7.5 7.5 7.5 7.5 7.5

region (-700< xt ≤500 and -800< xt ≤ 200) the cell size was reduced to twothirds of that of the medium mesh and in the very-near region of the pointsource the cell size was further reduced to approximately one third of that ofthe medium mesh.

Except in the near source region, the results from the medium mesh computa-tion were in good agreement with those from the fine mesh, which suggests agood degree of mesh independence. The discrepancy in the near source regionis almost certainly due to the effect of the source size, which was effectively

12

0

0.05

0.1

0.15

0.2

0.25

-1000 -500 0 500 1000 1500 2000 2500

xt(mm)

CmU

refh

m2 /Q

s

z=10mm, LES

z=55mm, LES

z=14mm, Expt.

(a)

0

0.05

0.1

0.15

-1000 -500 0 500 1000 1500 2000 2500

xt(mm)

Crm

sUre

fhm

2 /Qs

z=10mm, LES

z=55mm, LES

z=14mm, Expt.

(b)

Fig. 11. Dimensionless mean and r.m.s. concentration along Marylebone Rd (i.e.along yt = 0). The source location is S5 and Qs is the source flux.

one grid size. Both sets of data are in reasonable agreement with the mea-surements, with values of concentration falling four decades from the sourceto station R8. However, at station R1 LES over-predicts the mean concen-tration. Note that in the absence of the buildings, R1 was the most remotestation from the plume core in terms of the ratio of the distance and the localplume width. At the remote edge of the plume, very high intermittency ofthe concentration signals occurs; this requires time-averaging durations longerthan those used if fully converged values are required.

A standard k − ε model was also used to predict point source dispersion overthe site. The same domain shown in Fig. 2 and the medium mesh were used.The inlet velocity, Reynolds stresses and length scales shown in Fig. 5 and 4were used to generate appropriate input profiles for the k − ε model. Fig. 10includes a comparison between LES and RANS of the predicted concentration,in which the k− ε model generally over-predicts the concentration, sometimesby an order of magnitude, at the ten R-locations. It was found that, (1) on thevertical cross section through the source and along the wind direction, RANSunderestimated the concentration above the urban canopy but overestimatedit within the canopy; (2) on a ground level horizontal cross section, RANSpredicted null concentration over a narrow street downstream of the source,whereas LES did not. This is probably partly due to the RANS’ weakness inprediction of a genuinely unsteady separation bubble at the corner of buildings.

Mean and fluctuating concentration along the main streets were also com-pared with measurements. Fig.11 is a typical example. Note that the tracerwas released at S5 (see Fig.10). In the absence of the buildings, the plumecore crossed the Marylebone Rd approximately at xt = 500. The locations ofthe peak mean concentration at heights zt = 110 (not shown here), 55 and10 are approximately xt=600, 800 and 1000 respectively. This suggests thatwithin the canopy the buildings affect the location of the peak mean con-centration more than above the canopy, which is perhaps not surprising. Theeastward shift of the location of the peak mean concentration could well bedue to a channelling effect (i.e. along Marylebone Rd). At the major inter-

13

section a secondary peak of mean concentration occured, which is due to thehigh concentration clouds coming from upstream along Gloucester Pl. Fig.11bshows a different pattern of the peaks – the strength of the peak of Crms atthe intersection was at least comparable with that at the core of the plume(i.e. approximately at xt=600). This could be due to the high intermittencyof the concentration signal at the intersection.

6 Numerical experiments

6.1 Sensitivity to source location and inlet conditions

Sensitivity of the local and far field mean concentration to the source locationwas investigated extensively. Concentrations arising from a source at S1 werecompared with those from a source at S2. The former is in the middle of YorkRd, whereas the latter is very close to the building on the north side, as shownin the inset in Fig.12. The mean concentration profiles over Marylebone Rdare essentially the same for the two sources. Note that in the absence of thebuildings the plume centre crossed the Marylebone Rd at xt=200. It is hardto discern any difference between the two peaks shown in Fig.12a. The crms

profiles shown in Fig.12b have the same pattern for the two sources, but somequantitative discrepancy.

Despite the similarities along the Marylebone Rd, significant differences werenoted in the near source regions. Fig.13 shows the local behavior of the con-centration dispersion for source S1. The high concentration clouds from S1,which was located in the middle of the road, were driven to the leeward walldue to the helical-type circulation flow in the street canyon shown in Fig.8.The scalar is thus more likely to be convected out of the canyon. Subsequently,the concentration is low on the intersection immediately downstream. Fig.14shows, on the other hand, the local behaviour of the concentration dispersionfor source S2, which was located close to the windward wall on the northside. Note that the convection effect of the helical-type circulation flow on theconcentration transport was less strong than that for the S1 source location.Less plume was ventilated out of the street canyon and consequently a highconcentration occurred at the intersection (York St - Thornton Pl) immedi-ately downstream. Very high concentration was found in the narrow street–Thornton Pl – toward the north.

Fig.15 shows a comparison of mean and r.m.s. concentration along MaryleboneRd for sources S3 and S4. The mean concentration profiles were essentiallythe same for the two source locations, except a quantitative discrepancy, e.g.at the major intersection. The two crms profiles were again essentially thesame. Fig.16 and Fig. 17 show the local dispersion behaviour for source S3and S4 source locations, respectively. Although both S3 and S4 are located in

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0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-1000 -500 0 500 1000 1500 2000 2500

xt(mm)

Cm

Ure

fhm

2 /Qs

z=55, -51.4deg,S2

z=55, -51.4deg,S1

z=10, -51.4deg,S2

z=10, -51.4deg,S1

(a)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-1000 -500 0 500 1000 1500 2000 2500

xt(mm)

Crm

sUre

fhm

2 /Qs

(b)

S2

S1

Fig. 12. Sensitivity to the location of the ground level sources at York St on dimen-sionless mean and r.m.s. concentration along Marylebone Rd.

S1

S1

(a) (b)Fig. 13. Mean concentration and wind vectors in the region near a source at S1. (a)a horizontal plane crossing S1; (b) a vertical plane crossing S1 and perpendicularto the York St.

S2

S2

(a) (b)

Fig. 14. As Fig.13, but for S2.

the middle of Gloucester Pl, the patterns of the contours are quite differentfor the two sources. For S3, the high concentration clouds were evidentlytransported towards the south (upstream) and also towards the west andthen upwards when approaching a building wall. This was partially due tothe effect of the immediate upstream intersection (York St - Goucester Pl).For S4, the dispersion process was dominated by the street canyon effect with

15

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-1000 -500 0 500 1000 1500 2000 2500

xt(mm)

Cm

Ure

fhm

2 /Qs

z=55, -51.4deg,S4

z=55, -51.4deg,S3

z=10, -51.4deg,S4

z=10, -51.4deg,S3

(a)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-1000 -500 0 500 1000 1500 2000 2500

xt(mm)

Crm

sUre

fhm

2 /Qs

(b)

S3

S4

Fig. 15. Sensitivity of the location of the ground level sources at Gloucester Pl ondimensionless mean concentration and concentration r.m.s. along Marylebone Rd.

S3

(a)

S3

(b)

Fig. 16. Mean concentration and wind vectors in the near region of source S3. (a)a horizontal plane through the source; (b) a vertical plane through the source andperpendicular to Gloucester Pl.

S4

S4

(a) (b)

Fig. 17. As Fig.16, but for S4.

weak convection towards the south. Interestingly, the plume width in the crossstreet direction for S4 is much less than that for S3 (see Fig.16b and Fig.17b),which might be because the along-street flow was stronger at the lower (S4)elevation than at S3.

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-51.40

R13: -0.04

R14: 0.04

R15: -0.25

R34: 0.63

R35: 0.56

R45: 0.48

Fig. 18. Sketch of the locations of the sources S1,S3,S4,S5 and the receptor R4, andcorrelation coefficients of concentration fluctuations at R4.

6.2 Correlation coefficient of two tracers

Study of the correlation coefficients arising from two (separately identifiable)tracers released from different continuous sources is very helpful for under-standing dispersion from a line source – e.g. from moving vehicles. It is alsouseful for studying the chemical reaction of two species in the atmosphere.The correlation coefficient can be either positive or negative, enhancing orreducing (respectively) the total concentration fluctuation variance from thecombined sources, assuming the sources are of the same species. Four differentnon-reactive tracers, c1, c3, c4 and c5, were released simultaneously from S1(on York St), S3, S4 (on Gloucester Pl) and S5 (on Crawford St), respectively.Time series of the four tracers were recorded at station R4 (on Gloucester Pl– see Table 1 and Fig.18). The correlation coefficient of concentration fluctu-

ations of two tracers (e.g. m & n) can be defined as Rmn = c′mc′n/√

c′2m c′2n ,where overbars indicate time averages as usual and c′m, c′n are the concen-tration fluctuation of tracers from sources at Sm and Sn, respectively. Fig.18gives values of the resulting correlation coefficients.

R34 is quite high, at 0.63, which is not surprising as S3 and S4 were only 100mmapart. However both R13 and R14 are very low, probably because of the largeangle between the line S1-S3 (or S4) and the wind direction, and neither stationS3 nor S4 is in the core of the plume from source S1. Note that, consideringthe channelling effect of Gloucester Rd, the local wind direction within thecanopy turns anti-clockwise a little for the −51.4◦ direction, looking down inFig.1, and also there is a tall and large building block located between S1 andS3. R35 and R45 are a little lower at 0.56 and 0.48, respectively. However, notethat the street distance between S5 and S3 or S4 is greater than that betweenS1 and S3 or S4. It should also be noted that stations S3 and S4 are both inthe core of the plume from source S5 (again considering the channelling effectof Gloucester Pl), which suggests that concentration signals from sources S5and S3/S4 are correlated by eddies along their streamwise axes; the turbulenceintegral length scale in the streamwise direction is a few times greater than

17

those in cross wind directions. On the other hand, plumes from S1 and S5alternatively pass the station R4 due to the plume meandering driven bylarge eddies and the channelling effect of the Gloucester Pl, and this generatesa negative correlation coefficient R15 = -0.25.

In their field experiments Hamilton (2007) investigated the correlation coef-ficients of concentration signals from twin sources on Marylebone Rd, withreceptors placed downwind up to three rows of blocks from the sources, andwith wind directions −90◦ or 90◦ – both perpendicular to Marylebone Rd. Intheir results, the separation scales of the correlation coefficient profiles wereon the order of the mean building height. In the current LES with the sourceslocated on different streets and with wind direction −51.4◦, the behaviour ofthe correlation coefficients of concentration signals from two sources presentsa more complicated picture, emphasising that such results are strongly depen-dent on local geometry and the specific wind direction.

7 Final Discussions and Conclusions

From the above, we draw six major conclusions. (1) LES with a resolutiondown to one meter in space and one second in time at full scale can givereasonable turbulence and scalar statistics of urban-type environments. (2) Itis crucial to have a proper inflow generator for such situations; other com-putations (not shown here) indicated conclusively that mean & fluctuatingvelocities are quite different from those obtained using inadequate temporaland spatial boundary conditions. Indeed, we have also tried using a periodicin-outlet boundary condition for this geometry and we found the LES resultswere not in reasonable agreement with the wind tunnel data. The problemmight be due to the model formulation, e.g. the domain length and domaindepth. For example, at the outlet London’s Regent’s Park (see Fig.1) is situ-ated, where the flow profile must immediately adjust to a profile with smallerroughness length. Furthermore, the inflow conditions adopted in the LES arealso more similar to that of the wind tunnel model, where upwind of theDAPPLE site, a large number of two-dimensional roughness elements wereinstalled. (3) However, subject to a proper estimation of mass flow at theinlet within the canopy region, an accurate specification of inlet turbulencefluctuations below the mean building height is not crucial. So, for example,the flow and the scalar dispersion results in the near region of the intersectionof Marylebone Rd and Gloucester Pl were not sensitive to the arrangementof the arrays of artificial blocks installed upstream of the DAPPLE site. (4)The flow details within and immediately above the canopy layer are highlydependent on the arrangement and the size of local individual blocks. (5) Thescalar dispersion in the near field (i.e. within a distance of O(h) of the source)is sensitive to the location of the source, whereas in the far field it is not.(6) The correlation coefficient of the concentration signals from two sourcesat different locations, at least for a wind direction of −51.4◦, presents a com-

18

plicated picture whose details depend significantly on the local geometry andthe wind direction. Our main conclusion is that LES, with an appropriateinflow technique, can produce satisfactory and affordable simulations of flowand scalar dispersion within and above usefully-sized sub-domains of a cityregion. There is no reason to suppose that these conclusions would not holdfor any other specific urban conurbation.

Acknowledgment: This project was supported by NERC under the UrbanMeteorology theme of the Universities Weather Research Network (UWERN,Grant No. DST/26/39 and, more recently, NCAS, Grant No.R8/H12/38). Wethank Dr Paul Hayden, of the EnFlo laboratory, University of Surrey, whoprovided the wind tunnel experimental data and with whom we had helpfuldiscussions. The computations were performed on the Iridis computationalsystem, University of Southampton.

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